Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
140 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 10. Dic30 | C4 | semidirect |
| 11. C5×Dic6 | C4 | semidirect |
| 13. #1204 | C4 | semidirect |
| 23. ΓL(1,𝔽16) | Q8 | semidirect |
| 53. Dic6 | AGL(1,𝔽5) | semidirect |
| 67. C3×C5 | C4×Q8 | semidirect |
| 90. C5 | #887 | semidirect |
| 99. C3 | Q8×AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×Dic6 | 2 |
| C4×ΓL(1,𝔽16) | 2 |
| C3×C4⋊AGL(1,𝔽5) | 2 |
| Dic3⋊AGL(1,𝔽5) | 2 |
| Dic3×AGL(1,𝔽5) | 2 |
| Q8×AGL(1,𝔽5) | 3 |
| #887 | 5 |